Kardar-Parisi-Zhang equation in one dimension and line ensembles

Pramana - Journal of Physics

Volumn 64, Issue 6 SPEC. ISS., 2005, Pages 847-857

  Spohn, Herbert ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Exact solution; Probability density functions; Two point function

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PROBABILITY DENSITY FUNCTION; RANDOM PROCESSES; SET THEORY;

EXACT SOLUTION; KARDAR-PARISI-ZHANG EQUATIONS; STOCHASTIC DYNAMICS; TWO-POINT FUNCTION;

DIFFERENTIAL EQUATIONS;

EID: 21544462586     PISSN: 03044289     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02704147     Document Type: Conference Paper

References (28)

1. M Kardar, G Parisi and Y Z Zhang, Phys. Rev. Lett. 56, 889 (1986)
2. K Johansson, Comm. Math. Phys. 209, 437 (2000)
3. K Johansson, The arctic circle boundary and the Airy process, arXiv:math.PR./0306216, to appear in Ann. Prob.
4. K Johansson, Comm. Math. Phys. 242, 277 (2003)
5. T Sasamoto and T Imamura, J. Stat. Phys. 115, 749 (2004)
6. P L Ferrari, Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues, arXiv:math-ph/0402053
7. P Ferrari and H Spohn, J. Stat. Phys. 113, 1 (2003)
8. A Rákos and G M Schütz, Current distribution and random matrix ensembles for an integrable asymmetric fragmentation process, arXiv:cond-mat/0405464
9. T Nagao and T Sasamoto, Asymmetric simple exclusion process and modified random matrix ensembles, arXiv:cond-mat/0405321
10. T Imamura and T Sasamoto, Fluctuations of the one-dimensional polynuclear growth model with external sources, arXiv:math-phys/0406001
11. P L Ferrari, M Prähofer and H Spohn, Stochastic growth in one dimension and Gaussian multi-matrix models, in Proceedings ICMP14 edited by J-C Zambrini, to be published
12. H van Beljeren, R Kutner and H Spohn, Phys. Rev. Lett. 54, 2026 (1985)
13. M Prähofer and H Spohn, Current fluctuations In the totally asymmetric simple exclusion process, in In and out of equilibrium edited by V Sidoravicius (Birkhäuser, Boston, 2002)
14. J Baik and E M Rains, Symmetrized random permutations, random matrix models and their applications (Cambridge University Press, 2001) vol. 40, pp. 1-19
15. C A Tracy and H Widom, J. Stat. Phys. 92, 809 (1998)
16. M Prähofer and H Spohn, J. Stat. Phys. 108, 1071 (2002)
17. M Prähofer and H Spohn, J. Stat. Phys. 115, 255 (2004)
18. P L Ferrari and H Spohn, Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process, arXiv:math-phys/ 0504041
19. F J Dyson, J. Math. Phys. 3, 1191 (1962)
20. M L Mehta, Random matrices, 2nd ed. (Academic Press, San Diego, 1991)
21. C A Tracy and H Widom, Differential equations for Dyson processes, arXiv:math-PR/0309082
22. C Schensted, Canad. J. Math. 16, 179 (1961)
23. J Wishart, Biometrika A20, 32 (1928)
24. S A Janowsky and J L Lebowitz, J. Stat. Phys. 77, 35 (1994)
25. M Ha, J Timonen and M den Nijs, Phys, Rev. E68, 056122 (2003)
26. K Johansson, Prob. Theory Rel. Fields 116, 445 (2000)
27. T Hwa and T Nattermann, Phys. Rev. B51, 455 (1995)
28. L-H Tang and I F Lyuksyutov, Phys. Rev. Lett. 71, 2745 (1993)